Question

N.Y. Lottery Numbers Come Up 9-1-1 on 9/11" was the headline of an article that appeared in the San Francisco Chronicle (September 13,2002 ). More than 5600 people had selected the sequence \(9-1-1\) on that date, many more than is typical for that sequence. A professor at the University of Buffalo is quoted as saying, "I'm a bit surprised, but I wouldn't characterize it as bizarre. It's randomness. Every number has the same chance of coming up." a. The New York state lottery uses balls numbered \(0-9\) circulating in three separate bins. To select the winning sequence, one ball is chosen at random from each bin. What is the probability that the sequence \(9-1-1\) is the sequence selected on any particular day? (Hint: It may be helpful to think about the chosen sequence as a threedigit number.) b. What approach (classical, relative frequency, or subjective) did you use to obtain the probability in Part (a)? Explain.

Short answer

The probability of drawing the sequence 9-1-1 in the lottery on any given day is 0.001 (or 1 in 1000). The approach used to calculate this probability was the classical approach.

Step-by-step solution

Calculate the probability for one draw

Accept that any ball chosen from a bin is a singular and independent event. As there are 10 balls (0-9) in each bin, the probability of drawing any particular number (e.g. 9, 1, or 1) is \(1/10 = 0.1\). Therefore, the probability of drawing a 9 from one bin, a 1 from another, and a 1 from the third is \(0.1 \times 0.1 \times 0.1\).

Multiply the probabilities of each draw

Given that these draws are independent events, the probabilities multiply. Thus, \(0.1 \times 0.1 \times 0.1 = 0.001\). This is the probability of drawing the sequence 9-1-1.

Identify the approach used

To answer part (b), analyzing how the probability was obtained, recognize you used the classical approach because there was a finite, equally likely set of outcomes and the probability was calculated theoretically.